IRT (item response theory)

Explore the relationship between unobserved latent characteristics such as mathematical aptitude and the probability of correctly answering test questions (items). Or explore the relationship between unobserved health and self-reported responses to questions about mobility, independence, and other health-affected activities. IRT can be used to create measures of such unobserved traits or place individuals on a scale measuring the trait. It can also be used to select the best items for measuring a latent trait. IRT models are available for binary, graded, rated, partial-credit, and nominal response items. Visualize the relationships using item characteristic curves, and measure overall test performance using test information functions. And much more.

Learn about IRT (item response theory).

Binary response models

One-parameter logistic (1PL)
Two-parameter logistic (2PL)
Three-parameter logistic (3PL)

Watch One-parameter logistic (1PL) models.
Watch Two-parameter logistic (2PL) models.
Watch Three-parameter logistic (3PL) models

Ordinal response models

Graded response
Partial credit
Generalized partial credit
Rating scale

Watch Graded response (GRM) models.
Watch Rating scale (RSM) models.

Categorical response model

Nominal response

Watch Nominal response (NRM) models.

Hybrid models with differing response types

Multiple-group IRT models

Allow parameters to vary across groups
Constrain parameters across groups to be equal
Available for all IRT models
Test for differences across groups

Watch IRT models for multiple groups.

Graphs

Item characteristic curves and boundary characteristic curves

Plot midpoint probabilities

Category characteristic curves
Test characteristic curve

Plot expected score for a specified ability level
Plot ability for a specified expected score

Item information functions
Test information function

Plot the standard error

Fully customizable graphs
Save your graphed results as datasets for future use

DIF diagnostics

Mantel–Haenszel test
Logistic regression test
IRT model-based test

Control panel interface

Access all IRT features
Easily select response type and item variables
Even create hybrid models
Estimate models
Select and customize graphs
Manage reporting of results

Control how your output is displayed

Sort by difficulty
Sort by discrimination
Group estimates by type or by item
Show results only for selected items
Compare IRT estimates across groups

Postestimation Selector

View and run all postestimation features for your command
Automatically updated as estimation commands are run

Watch Postestimation Selector.

Additional resources

Item Response Theory Reference Manual
A Course in Item Response Theory and Modeling with Stata by Tenko Raykov and George A. Marcoulides
In the spotlight: irt
In the spotlight: Bayesian IRT—4PL model

Watch IRT (item response theory) models.

See New in Stata 18 to learn about what was added in Stata 18.

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